Study On The Faring Of Ship NURBS Curves And Surfaces Based On Wavelet Theory

Hull line fairing is the basis and core of ship design and is the key to realizing the aim of ship design, which includes fairing of hull curve and surface. Due to the un-unified fairing concept and unperfected fairing criteria, the study on the fairing of free curve and surface is less now. Moreover, the complicated hull shape and the restraint condition of practical engineering decide the complication of free curve and surface fairing. Therefore the algorithm of free curve and surface fairing can't meet the demand of hull lines design. Wavelet Transform is an integrated fairing method, which has the merits of high data compress and work efficiency and being fit for fairing curve and surface with plenty of control vertexes. Therefore wavelet transform is chosen as the theory basis of hull curve and surface fairing. The paper studies the one-dimensional and two-dimensional NURBS wavelet transforms deeply which are used as the smoothing method of ship curve and surface. The main work and contributions of the paper are as follows:(1) The paper introduces and importance of the study on ship curve and surface fairing, and explains the present situations, methods and existed problems of the fairing of free curve and surface and ship curve and surface.(2) The fairing concept is summarized and three concepts are proposed mathematical fairing, physical fairing and functional fairing. On the basis of this and the characteristics of ship curve and surface, the criteria of ship curve and surface are defined.(3) Wavelet transform is deeply studied, and NURBS curve and surface wavelets are constructed to fair ship curve and surface. Since NURBS function satisfies wavelet frame theory, it can be used to construct NURBS wavelet (the rational basis function of NURBS function as the scale function, and NURBS function as wavelet function). Differing from free curve and surface, ship curve and surface are with a certain constraint conditions, so the practical constraint conditions should be considered in fairing process. The paper contrasts the methods of wavelet transform and points reduced method, which shows the advantage of wavelet transform in curve fairing. But there still exist some problems. To overcome the intrinsic defects of wavelet transform, the paper presents Wavelet Transform with Constrains (WTC), Wavelet Least Square Method (WLSM) and Wavelet Energy Method (WNM) to fair ship curve, and presents the method of combining wavelet transform and constrains to fair ship surface. (4) Wavelet Neural Network is used to approximate ship curve and surface. Intelligent algorithms like BP Neural Network and RBF Neural Network are also applied in free curve and surface fairing. In contrast with these algorithms, Wavelet Neural Network has better features (high approximate speed, single solution and etc.), so it is more suitable for fairing free curve and surface. The paper introduces the construct principle of multi-resolution wavelet network, uses NURBS function and NURBS basis function separately as wavelet function and scale function, and constructs one-dimensional and two-dimensional multi-resolution B-sample Wavelet Neural Network. According to the characteristics of ship curve and surface, the network target functions are given, and gradient algorithm is used to train the sample to approximate ship curve and surface.(5) The improved wavelet transform algorithm is used to fair hull line. With certain ship main scales, hull design includes the design of section area curve, design waterline, aft and fore lines, section line, bow, stern and etc. To overcome the shortcoming of the shift of aft and fore points of wavelet transform, the paper firstly improves the wavelet algorithm, and proposes the calculating methods of multi-resolution open curve area and abscissa of curve centroid. Secondly the improve wavelet transform is used to fair section area curve and section line in consideration of their features, so as to obtain satisfied hull lines.It is proved by the study and calculating examples that the successful combination of NURBS theory and wavelet theory becomes the basis of ship curve and surface fairing. On this basis, other mature algorithms (eg. Least Square Method, Energy methods and neural network) are combined to fair ship curve and surface with high speed and efficiency.